On Deep Option Pricing in Local Volatility Models

Sergey Shorokhov
We study boundary value problem for Black-Scholes-Merton partial differential equation for a European call option price, when volatility depends on asset price and time (local volatility model). An approximation to option price is obtained via deep learning with deep Galerkin method (DGM). For some cases with known exact closed-form solutions analytical option prices and their DGM approximations are compared.